Embedded model control GNC for the Next Generation Gravity Mission

Abstract

A Next Generation Gravity Mission (NGGM) concept for measuring the Earth's variable gravity field has been recently proposed by ESA. The mission objective consists in measuring the temporal variations of the Earth gravity field over a long time span, with very high spatial and temporal resolutions. This paper focuses on the guidance, navigation and control (GNC) design for the science phase of NGGM mission. NGGM will consist of a two-satellite long-distance formation like GRACE, where each satellite will be controlled to be drag-free like GOCE. Satellite-to-satellite distance variations, encoding gravity anomalies, will be measured by laser interferometry. The formation satellites, distant up to 200 km, will fly in a quasi-polar orbits at an Earth altitude between 300 and 450 km. Orbit and formation control counteract bias and drift of the residual drag-free accelerations, in order to reach orbit/formation long-term stability. Drag-free control allows the formation to fly counteracting the atmospheric drag, ideally subject only to gravity. Orbit and formation control, designed through the innovative Integrated Formation Control (IFC), have been integrated into a unique control system, aiming at stabilizing the formation triangle consisting of satellites and Earth Center of Masses. In addition, both spacecraft must align their control axis to the satellite-to-satellite line (SSL) with micro-radiant accuracy. This is made possible by specific optical sensors and the inter-satellite laser interferometer, capable of materializing the SSL. Such sensors allow each satellite to pursue an autonomous alignment after a suitable acquisition procedure. Pointing control is severely constrained by the angular drag-free control which must ideally zero the angular acceleration vector, in the science frequency band. The control unit has been designed according to the Embedded Model Control methodology and is organized in a hierarchical way, where drag-free control plays the role of a wide-band inner loop, and orbit/formation and attitude/pointing controls are narrow band outer loops. The relevant state equations are converted to discrete time providing the embedded model, part of the control unit. The state predictor, control law and reference generator are built on and interfaced to the embedded model. Simulated results, via a high-fidelity simulator, prove the concept validity and show that the control performances are in agreement with the defined mission requirements. Indeed, the presented control strategy has been shown capable of keeping the attitude and formation variables stable within the required boundaries, all over the 10-year mission, through a low-thrust authority in the order of few milli-Newton.

Earth Gravity In-Orbit Sensing: MPC Formation Control Based on a Novel Constellation Model

“…Specifically, the orbital dynamics is a special form of the Hill-Clohessy-Wiltshire equations [22,23]. Such formulation, described in detail in [24], is based on the definition of a peculiar formation reference frame (the Formation Local Orbital Frame, FLOF) and the formation triangle virtual structure [21]. These, in turn, lead to the derivation of a novel set of equations describing the spacecraft's orbit and constellation dynamics.…”

“…The first two constraints in the optimization problem (25) ensure that the predicted state and output are consistent with the system's Equation (24), while X C , Y C , and U C are suitable sets describing possible constraints on the state, output, and input, respectively. The performance index J is a weighted quadratic function of the predicted output tracking error ỹp and system input ũ.…”

“…The predicted tracking error is ỹp (τ) = r(τ) − ỹ(τ), whereas r(τ) is the desired reference to track and ỹ(τ) is obtained by the integration of Equation (24). The weights Q ≥ 0, P ≥ 0, and R ≥ 0 are diagonal matrices.…”

“…Such a formulation, called Triangle Dynamics (TD), allows the derivation of ad hoc differential equations for the description of the spacecraft's orbit and constellation dynamics. The choice is motivated by the advantage of describing a unique formulation for both the orbit and constellation dynamics [21]. The TD model is compared in simulation with a standard model and is based on the well-known Hill-Clohessy-Wiltshire (HCW) equations.…”

A 3D heterogeneously integrated guidance, navigation, and control micro-system

“…Guidance, navigation, and control (GNC) systems are the key modules of aircraft and robots. [1][2][3][4][5][6][7][8] Traditionally, GNC is divided into three parts-namely, a guidance sub-system, a navigation sub-system, and a control sub-system. Now micro UAVs and small robots require electronic systems that reduce volume and increase performance sharply.…”